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Threshold Results for U-Statistics of Dependent Binary Variables

Becker, Niels; Utev, Sergey

Description

Large sample results for certain U-statistics, and related statistics, of binary dependent random variables are studied. The class of U-statistics include partial sums and polynomials of partial sums of a sequence of random variables. A very wide range of limit results are found. The form of the limit result can depend substantially on the magnitude of the appropriate normalizing sequence for the sum. Unexpectedly, the nature of the limit result also depends significantly on whether the degree...[Show more]

dc.contributor.authorBecker, Niels
dc.contributor.authorUtev, Sergey
dc.date.accessioned2015-12-13T23:20:39Z
dc.identifier.issn0894-9840
dc.identifier.urihttp://hdl.handle.net/1885/90803
dc.description.abstractLarge sample results for certain U-statistics, and related statistics, of binary dependent random variables are studied. The class of U-statistics include partial sums and polynomials of partial sums of a sequence of random variables. A very wide range of limit results are found. The form of the limit result can depend substantially on the magnitude of the appropriate normalizing sequence for the sum. Unexpectedly, the nature of the limit result also depends significantly on whether the degree of the U-statistic is even or odd. It is shown that dependence is a major factor contributing to this result. The limit results are illustrated with reference to a simple dynamic sequence of binary variables and a reinforced random walk.
dc.publisherPlenum Publishing Corporation
dc.sourceJournal of Theoretical Probability
dc.subjectKeywords: Dependent binary variables; Threshold results; U-statistics
dc.titleThreshold Results for U-Statistics of Dependent Binary Variables
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume14
dc.date.issued2001
local.identifier.absfor111706 - Epidemiology
local.identifier.ariespublicationMigratedxPub21269
local.type.statusPublished Version
local.contributor.affiliationBecker, Niels, College of Medicine, Biology and Environment, ANU
local.contributor.affiliationUtev, Sergey, College of Medicine, Biology and Environment, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage97
local.bibliographicCitation.lastpage114
local.identifier.doi10.1023/A:1007821131604
dc.date.updated2015-12-12T09:03:59Z
local.identifier.scopusID2-s2.0-0035630680
CollectionsANU Research Publications

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